Solve for $x$ and $y$ using elimination. ${-x-5y = -8}$ ${x-4y = -1}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-9y = -9$ $\dfrac{-9y}{{-9}} = \dfrac{-9}{{-9}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x-5y = -8}\thinspace$ to find $x$ ${-x - 5}{(1)}{= -8}$ $-x-5 = -8$ $-x-5{+5} = -8{+5}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 1}$ into $\thinspace {x-4y = -1}\thinspace$ and get the same answer for $x$ : ${x - 4}{(1)}{= -1}$ ${x = 3}$